Question: Rewrite as a simplified fraction. ${2.6\overline{92} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2692.9292...\\ 10x &= 26.9292...\end{align*}}$ Subtracting the two equations, we have: ${990x = 2666}$ ${x = \dfrac{2666}{990}} $ ${x = \dfrac{1333}{495}} \text{or} {2 \dfrac{343}{495}}$